I am sorry to read about the problem with the XPS 13. This could be a Video card / driver problem or a defect with the LCD screen. If you have an external monitor to test, hook it up to the system and see if you notice the problem on the external monitor. If you have the problem on both the LCD and the external monitor then the issue is either with the Video driver or the GPU. I first suggest that you reinstall the video driver. The newest driver for the XPS 13 may be found from the following link.

If you have the issue on the LCD screen but the external monitor looks good then the problem is with the LCD screen and a service will be needed. If you wish, shoot me a private message with the service tag of your notebook, your name, address, email address and phone number and I will be happy to research possible service options.

There really isn't an easy way to fix this on your own but firstly, test your laptop with an external monitor to see if those blotches appear on it too. If it doesn't appear on the external monitor then your laptop screen has problems.

I had to change my whole screen but it didn't take very long, probably only 30 mins. Since mine was under warranty at that time, Dell changed it for free.

You can call their customer care line to tell them about the problem and they'll assist you.